120 psi should be enough to start and run OK.
Pinch off the fuel line and pull the rope till it starts. If it starts then the carb is flooding.
If it doesn't start , then you either have a spark issue or leaking crank seals or headgasket.
Did you get the coil gapped correctly. ? Did you check for any side movement on the flywheel when you checked the key ? Is there any crank noise when you pull the rope ?